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Search: id:A078136
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| A078136 |
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Numbers having exactly one representation as sum of squares>1. |
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+0
8
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| 4, 8, 9, 12, 13, 17, 18, 21, 22, 26, 27, 30, 31, 35, 39
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A078134(a(n))=1.
The sequence is finite with a(15)=39 as last term, since numbers m>39 can be represented as sums of squares>1 (even of squares of primes and even of squares of 2, 3 and 4 and even of squares of 2, 3 and 5) in at least two ways. Proof: if m=40+4k, k>=0, then m=(k+10)*2^2=(k+1)*2^2+4*3^2; if m=41+4k, then m=(k+8)*2^2+3^2=(k+4)*2^2+5^2; if m=42+4k, then m=(k+6)*2^2+2*3^2=(k+2)*2^2+3^2+5^2; if m=43+4k, then m=(k+4)*2^2+3*3^2=k*2^2+2*3^2+5^2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Nov 11 2007
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LINKS
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Eric Weisstein's World of Mathematics, Square Number.
Index entries for sequences related to sums of squares
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CROSSREFS
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Cf. A000290, A078137, A078135, A078130.
Cf. A078134, A078139, A090677, A078137, A134754, A134755.
Sequence in context: A158758 A078137 A010453 this_sequence A037973 A044844 A145190
Adjacent sequences: A078133 A078134 A078135 this_sequence A078137 A078138 A078139
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KEYWORD
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nonn,fini,full
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 19 2002
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